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3 years ago

Calculate the area of the shapes below.

Mathematics

2 answers:

olganol [36]3 years ago

8 0

Answer:

24 ft

Step-by-step explanation:

1/2hb

4=h

12=b

plug in

1/2(4)(12)= 24

GREYUIT [131]3 years ago

6 0

Answer:

the answer should be 24ft

Step-by-step explanation:

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Evaluate integral _C x ds, where C is

borishaifa [10]

Answer:

a. $\mathbf{36 \sqrt{5}}$

b. $\mathbf{ \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}$

Step-by-step explanation:

Evaluate integral _C x ds where C is

a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)

i . e

$\int \limits _c \ x \ ds$

where;

x = t , y = t/2

the derivative of x with respect to t is:

$\dfrac{dx}{dt}= 1$

the derivative of y with respect to t is:

$\dfrac{dy}{dt}= \dfrac{1}{2}$

and t varies from 0 to 12.

we all know that:

$ds=\sqrt{ (\dfrac{dx}{dt})^2 + ( \dfrac{dy}{dt} )^2}} \ \ dt$

∴

$\int \limits _c \ x \ ds = \int \limits ^{12}_{t=0} \ t \ \sqrt{1+(\dfrac{1}{2})^2} \ dt$

$= \int \limits ^{12}_{0} \ \dfrac{\sqrt{5}}{2}(\dfrac{t^2}{2}) \ dt$

$= \dfrac{\sqrt{5}}{2} \ \ [\dfrac{t^2}{2}]^{12}_0$

$= \dfrac{\sqrt{5}}{4}\times 144$

= $\mathbf{36 \sqrt{5}}$

b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)

Given that:

x = t ; y = 3t²

the derivative of x with respect to t is:

$\dfrac{dx}{dt}= 1$

the derivative of y with respect to t is:

$\dfrac{dy}{dt} = 6t$

$ds = \sqrt{1+36 \ t^2} \ dt$

Hence; the integral _C x ds is:

$\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt$

Let consider u to be equal to 1 + 36t²

1 + 36t² = u

Then, the differential of t with respect to u is :

76 tdt = du

$tdt = \dfrac{du}{76}$

The upper limit of the integral is = 1 + 36× 2² = 1 + 36×4= 145

Thus;

$\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt$

$\mathtt{= \int \limits ^{145}_{0} \sqrt{u} \ \dfrac{1}{72} \ du}$

$= \dfrac{1}{72} \times \dfrac{2}{3} \begin {pmatrix} u^{3/2} \end {pmatrix} ^{145}_{1}$

$\mathtt{= \dfrac{2}{216} [ 145 \sqrt{145} - 1]}$

$\mathbf{= \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}$

5 0

3 years ago

Y=2x-5, The slope is ............ 0 0 D 2 2 o -5 0 -3

pogonyaev

Answer: 2

Step-by-step explanation:

The given equation is in slope-intercept form. It is y=mx+b. In this equation, m stands for slope and b stands for y-intercept. Looking back at the equation, we see that in place of m is 2. That tells us that the slope is 2.

5 0

3 years ago

Read 2 more answers

WILL GIVE BRAINLIST SOON AS I CAN... I DON'T UNDERSTAND THIS

enot [183]

Answer:

z would equal 20°

Step-by-step explanation:

This means ACB and EFD are 2 similar triangles

They have the same shape but different size

In ACB because 3 corner of a traingle must = 180° so in this case, corner BAC would = 180 - 65 - 55 = 60°

As you can see, BC is 3 times as large as DF, this means triangle ACB is larger than triangle EFD 3 times, this would lead to corner BAC is larger than corner DEF 3 times.

Corner DEF would = corner BAC / 3

= 60° / 3

= 20°

SO z would equal 20°

Hope this helped :3

7 0

3 years ago

Read 2 more answers

Can someone please help me with my homework and explain it to me I will mark as brainlyist

Keith_Richards [23]

Answer:

121.76

Step-by-step explanation:

the original price is 83.97. you would have to find 45% of that. you would do this by putting x/83.97= 45/100

multiply 45 and 83.97 to get 3778.65. then divide that by 100 to get 37.7865. Add that to 83.97 to get 121.7565. round it to the nearest hundreth to get the total of 121.76 dollars

mark as brainlyest and answer my question

8 0

3 years ago

Which of the numbers below is not the same as the others ?

ExtremeBDS [4]

Perecen means parts out of 100
convert everybody to decimal

1/8=0.125
12.5=12.5
12.5%=0.125
1/8=0.125

the different one is B

3 0

4 years ago

Read 2 more answers