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2 years ago

Find the missing side of this right triangle.

Mathematics

1 answer:

AleksandrR [38]2 years ago

4 0

Answer:

x = sqrt(403)

Step-by-step explanation:

Use Pythagorean Theorem for right triangles

x^2 + 9^2 = 22^2

x = sqrt 403

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When records were first kept (t=0), the population of a rural town was 260 people. During the following years, the population gr

Firdavs [7]

Answer:

(a) The population after 15 years is 2678.

(b)Therefore the population P(t) at any time t>0 is

$P(t)= 45t+30 {t^{\frac32}}+260$

Step-by-step explanation:

Given that,

The population grew at a rate of

$P'(t)=45(1+\sqrt t)$

Integrating both sides

$\int P'(t) dt=\int 45(1+\sqrt t)dt$

$\Rightarrow \int P'(t) dt=\int (45+45\sqrt t)dt$

$\Rightarrow \int P'(t) dt=\int 45\ dt+\int 45\sqrt t\ dt$

$\Rightarrow P(t)= 45t+45\ \frac{t^{\frac12+1}}{\frac12+1}+c$ [ c is integration constant]

$\Rightarrow P(t)= 45t+45\ \frac{t^{\frac32}}{\frac32}+c$

$\Rightarrow P(t)= 45t+45\times\frac 23 \times {t^{\frac32}}+c$

$\Rightarrow P(t)= 45t+30 {t^{\frac32}}+c$

When t=0 , P(0)= 260

$\therefore 260= 45\times0+30\times {0^{\frac32}}+c$

$\Rightarrow c=260$

$\therefore P(t)= 45t+30 {t^{\frac32}}+260$

Therefore the population P(t) at any time t>0 is

$P(t)= 45t+30 {t^{\frac32}}+260$

To find the population after 15 years, we need to plug t=15 in the above expression.

$P(15)=( 45\times 15)+30( {15^{\frac32}})+260$

≈2678

The population after 15 years is 2678.

5 0

3 years ago

Find the measure of line segment TU. Assume that lines which appear to be tangent to the circle are tangent.

Sedaia [141]

Given:

A figure of a circle. A secant SU and a tangent SR is drawn to the circle from the external point S.

To find:

The measure of the line segment TU.

Solution:

According to the secant tangent segment theorem, the square of tangent is equal to the product of secant and external segment of the secant.

Using secant tangent segment theorem, we get

$SR^2=SU\times ST$

$(40)^2=(32+2x-2)\times (32)$

$1600=(30+2x)(32)$

$1600=960+64x$

Subtract both sides by 960.

$1600-960=64x$

$640=64x$

Divide both sides by 64.

$\dfrac{640}{64}=x$

$10=x$

Now, the measure of the line segment TU is:

$TU=2x-2$

$TU=2(10)-2$

$TU=20-2$

$TU=18$

Therefore, the correct option is C.

6 0

3 years ago

Does anyone know this pls help

statuscvo [17]

Y = 3/4x + 4

Y = mx + b

m = slope (6/8)
b = y intercept (4)

7 0

3 years ago

Read 2 more answers

Name the place of the highlighted digit. then write the value of the digit 35.052

AysviL [449]

Solution:

Given: 35.052

The standard form is: 35.052

3 is in the tens place. 3 = 3 × 1

5 is in the tens place. 5 = 5 × 1

0 is in the tenths place. 0.0 = 0 × 1/10

5 is in the tenths place. 0.05 = 5 × 1/100

2 is in the tenths place. 0.002 = 2 × 1/1000

7 0

4 years ago

Read 2 more answers

Hi I need to find DO length

MakcuM [25]

Answer:

10 cm

Step-by-step explanation:

If we assume that DC is parallel to AB, then triangle DOC is similar to triangle AOB.

However, even with this assumption, there is not enough information in the diagram to solve for DO. We would also need to know the length of CO. Then we could write a proportion:

DO / (DO + 20) = CO / (CO + 24)

Edit: OD is 2 cm shorter than OC. If we call x the length of OD, then the length of OC is x+2.

Putting this into our proportion:

x / (x + 20) = (x + 2) / (x + 2 + 24)

x / (x + 20) = (x + 2) / (x + 26)

Cross multiply:

x (x + 26) = (x + 2) (x + 20)

Distribute:

x² + 26x = x² + 20x + 2x + 40

x² + 26x = x² + 22x + 40

4x = 40

x = 10

So the length of DO is 10 cm.

4 0

3 years ago