Which event is important enough to include in a summary of this

HELPPP PLEASEEEEEEE

kkurt [141]

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

factorization of 45 is 5 x 3 x 3, or 5 x 3^2.

3 0

3 years ago

find the perimeter and diagonal of a square whose area is equal to the area of a rectangle whose length is 9m and breadth is 4m

aalyn [17]

$Area\ of\ a\ rectangle:A_{\fbox{ }}=9m\times4m=36m^2\\\\a-side\ of\ a\ square\\\\Area\ of\ a\ square:A_{\fbox{}}=a^2\\\\A_{\fbox{ }}=A_{\fbox{}}\Rightarrow a^2=36m^2\Rightarrow a=\sqrt{36m^2}\Rightarrow a=6m\\\\Perimeter\ of\ the\ square:P=4a\Rightarrow P=4\times6m=\boxed{24m}\\\\Diagonal\ of\ the\ square:d=a\sqrt2\Rightarrow d=\boxed{6\sqrt2\ m}$

4 0

3 years ago

Fred the owl is looking down at a 67° angle from the top of a tree that is 15 ft tall, when he spots a bird on the ground. How f

guapka [62]

Answer:

Fred C. 16.30 ft

Gary B. 169.67 m

Step-by-step explanation:

Fred the owl...

Always draw a diagram first (see diagram below). We assume trees are perpendicular (at 90°) to the ground. The situation forms a right-angle triangle.

We need to find "x", which is the direct distance between the owl and the bird. "x" is also the hypotenuse, which is the longest side in a right-angle triangle. Since we know a side and an angle, we can find the hypotenuse using primary trigonometry ratios.

∠B will be the angle of reference (the angle we are "talking" about). The side we know is opposite to ∠B (15ft). We know it's opposite because it's not touching the angle. The side we need to find is the hypotenuse.

Use the trig. ratio sine because it has opposite and hypotenuse in it. The general formula is:

sinθ = opp/hyp

θ means the angle, and we know it is 67°.

Replace all the information you know:

sinB = opp/hyp

sin67° = (15ft) / x Isolate "x". Rearrange the equation.

xsin67° = (15ft) Divide both sides by sin67°

x = (15ft) / sin67°

x = 16.295... ft Exact answer in decimals

x ≈ 16.30 ft Rounded to nearest hundredth

Therefore Fred the owl is 16.30 feet from the bird.

Gary spots a monkey...

Draw a diagram first (see below). G is Gary, M is the monkey, T is the bottom of the Sears Tower. We need to find "x", which is the distance between the monkey and the bottom of the tower.

The angle of reference is M, which is 69°. We need to find the adjacent side and we know the opposite side. The trig. ratio that has adjacent and opposite is tangent.

tanθ = opp/adj

Replace all the information you know:

tanM = opp/adj

tan69° = (442m) / x Rearrange the formula to isolate "x"

xtan69° = 442m Divide both sides by tan69°

x = 442m / tan69° Solve by dividing

x = 169.6679.... m Exact decimal answer

x ≈ 169.67m Rounded to the nearest hundredth

Therefore the monkey is 169.67 metres from the tower.

Remember all the trig. ratios using the acronym SohCahToa.

o = opposite side

a = adjacent side

h = hypotenuse side

S = sine, sin for short

C = cosine, cos for short

T = tangent, tan for short

The operation is always dividing the first side in the acronym by the second side.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

4 0

3 years ago

the mantle layer of earth begins about 70 kilometers underneath the surface. The layer called the outer core begins about 2970 k

gavmur [86]

Given:
mantle layer of earth begins about 70 kilometers underneath the surface
outer core begins about 2970 kilometers underneath the surface

Since we need to find the position of each layer relative to the surface, the surface will serve as the point of origin or 0. Below the surface infers a negative value. So, Mantle layer is -70 km from the surface while outer core is -2970 km under the surface.

Comparing -70 and -2970, -70 has a greater value than -2970. The nearer the number is to the origin or 0, the higher its value.

Comparing the absolute greater value of -70 and -2970, -2970 has a greater absolute value. This is because absolute value is the positive value of the number. Absolute value of -70 is 70 while absolute value of -2970 is 2970. Thus, -2970 has a greater absolute value.

6 0

2 years ago

how to integrate <img src="https://tex.z-dn.net/?f=e%5E%7B2s%7D%20%2ACos%20%5Cfrac%7Bs%7D%7B4%7D" id="TexFormula1" title="e^{2s}

icang [17]

Answer:

$\int\limits {e^{2s} cos\frac{s}{4} ds$ = $\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))$

Step-by-step explanation:

Step(i):-

Given that $f(s) = e^{2s} cos\frac{s}{4}$

Now integrating

$\int\limits {f(s)} \, ds = \int\limits {e^{2s} cos\frac{s}{4} ds$

By using integration formula

$\int\limits { e^{ax} cos b x dx = \frac{e^{ax} }{a^{2}+b^{2} } ( a cos b x + b sin b x )$

Step(ii):-

$\int\limits {e^{2s} cos\frac{s}{4} ds$ = $\frac{e^{2s} }{(2)^{2}+(\frac{1}{4}) ^{2} } ( 2 cos (\frac{1}{4} ) s + \frac{1}{4} sin \frac{1}{4} s ))$

= $\frac{e^{2s} }{(4+\frac{1}{16})} ( 2 cos (\frac{1}{4} ) s + \frac{1}{4} sin \frac{1}{4} s ))$

= $\frac{e^{2s} }{(\frac{65}{16} } ( \frac{8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s}{4} ))$

= $16 X\frac{e^{2s} }{65 } ( \frac{8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s}{4} ))$

= $\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))$

Final answer:-

$\int\limits {e^{2s} cos\frac{s}{4} ds$ = $\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))$

6 0

2 years ago