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3 years ago

What is the m∠2 if m∠4 = 81° and m∠3 = 40°? a. 40° b. 59° c. 41° d. 60°

Mathematics

2 answers:

velikii [3]3 years ago

8 0

Answer:

C. 41

Step-by-step explanation:

180 - 81 = 99

99+40 = 139

180 -139 = 41

Aleks04 [339]3 years ago

5 0

Answer: B. 59 degrees

You need to add Angle 4 which is 81 to Angle 3 which is 40

81+40=121 and then we will subtract it from 180

180-121=59 degrees

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A road perpendicular to a highway leads to a farmhouse located d miles away. An automobile traveling on this highway passes thro

pshichka [43]

Answer:

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+900}}$

Step-by-step explanation:

A road is perpendicular to a highway leading to a farmhouse d miles away.

An automobile passes through the point of intersection with a constant speed $\frac{dx}{dt}$ = r mph

Let x be the distance of automobile from the point of intersection and distance between the automobile and farmhouse is 'h' miles.

Then by Pythagoras theorem,

h² = d² + x²

By taking derivative on both the sides of the equation,

$(2h)\frac{dh}{dt}=(2x)\frac{dx}{dt}$

$(h)\frac{dh}{dt}=(x)\frac{dx}{dt}$

$(h)\frac{dh}{dt}=rx$

$\frac{dh}{dt}=\frac{rx}{h}$

When automobile is 30 miles past the intersection,

For x = 30

$\frac{dh}{dt}=\frac{30r}{h}$

Since $h=\sqrt{d^{2}+(30)^{2}}$

Therefore,

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+(30)^{2}}}$

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+900}}$

3 0

3 years ago

P=2^(43112609)-1 Suppose you have traveled to a faraway place where the base of the number system is 37 . (The inhabitants of th

AfilCa [17]

Answer:

8,275,842 digits

Step-by-step explanation:

One more than the floor of the logarithm to the base 37 gives the number of digits. The change of base formula can be used.

$\log_{37}{(2^{43112609}-1)}\approx\dfrac{43112609\log{2}}{\log{37}}\approx 8275841.2$

Expressed in the base-37 number system, P has 8275842 digits.

6 0

3 years ago

A man flies a kite at a height of 15 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. How fast

Misha Larkins [42]

Answer:

4.4 ft/s

Step-by-step explanation:

Height = 15ft

Rate= 5 ft/s

Distance from the man to the kite= 32ft

dh/dt = 5 ft/s

h = √32^2 - 15^2

h = √ 1025 - 225

h = √800

h = 28.28ft

D = √15^2 + h^2

dD/dt = 1/2(15^2 + h^2)^-1/2 (2h) dh/dt

= h(225 + h^2)^-1/2 dh/dt

= (h / √225 + h^2)5

= (28.28 / √225 + 28.28^2)5

= (28.28 / √1024.7584)5

= (28.28/32)5

= 0.88*5

= 4.4 ft/s

3 0

4 years ago

I bought a TV. the screen is 52 inches wide and 29 inches high. find the length of its diagonal.

Crank

Answer:

*3545*

Step-by-step explanation:

52 square + 29 square = 3545

then square root 3545 = 59.539 ( round it if you want)

6 0

3 years ago

Find the area of a trapezoid with bases of 15cm and 6 cm and a height of 1/5cm

NNADVOKAT [17]

Area = 0.5 x (a+b) x h

= 0.5 x (15cm + 6cm) x 1/5cm
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8 0

3 years ago

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