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2 years ago

In ΔVWX, v = 21 cm, w = 64 cm and ∠X=23°. Find the length of x, to the nearest centimeter.

Mathematics

2 answers:

just olya [345]2 years ago

7 0

Answer:

its b just toook the test

Step-by-step explanation:

Alla [95]2 years ago

6 0

Answer:

45 (in centimeters)

Step-by-step explanation:

In ΔVWX we have to find the length of the third side.

When the length of two sides of a triangle and the included angle is given

we can find the length of third side by applying cosine law.

According to cosine law, in a ΔVWX

$x^{2} =v^{2}+w^{2} -2vwcosX$

$=21^{2}+64^{2}-(2\times21\times64\times cos23)$

=2062.683 $(cm)^{2}$

$x=45$ cm (approximating it to nearest integer)

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What is YZ ? Enter your answer as a decimal in the box.

Jobisdone [24]

If you look at the figure, triangles XVW and ZYW are similar. So, you can use ratio and proportion to solve this problem. Notice that there are tick marks on th other two sides of the bigger triangles. That indicates that the like signs of ticks are equal. For example, that means XZ = ZW and that XW = 2XZ = 2ZW.

24.4/YZ = XW/ZW
24.4/YZ = 2ZW/ZW
24.4/YZ = 2
Solving for YZ,
YZ = 12.2

7 0

2 years ago

Read 2 more answers

The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

Lemur [1.5K]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Do, integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Substitute the value in 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Hence Cardiac output: $F=0.055 L\s$

4 0

2 years ago

Find the measure of ∠EGC. Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 50 degrees, the mea

miv72 [106K]

Answer:

m∠EGC=70°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite

m∠EGC=(1/2)[arc EC+arc DF]

Find the value of x

we have

m∠EGC=(7x+7)°

arc EC=50°

arc DF=10x°

substitute and solve for x

(7x+7)°=(1/2)[50°+10x°]

14x+14=50+10x

14x-10x=50-14

4x=36

x=9

Find the measure of angle EGC

m∠EGC=(7x+7)°

substitute the value of x

m∠EGC=(7(9)+7)°=70°

8 0

2 years ago

Read 2 more answers

3) Last year Kerry’s take home pay was £15 000 She spent 40% of her take home pay on rent. She used the rest of her take home pa

gregori [183]

3,000. You take 15,000 and multiply by .4 to get how much she spent on rent (6,000). They you subtract the rent money from her total pay to get her money that she spent on living expenses, clothes and entertainment in total (9,000). Since she spent her money in six parts (3+2+1), you divide 9,000 by 6 to get 1,500 to get each part. Since for entertainment she has two parts you multiply 1,500 by 2 to get 3,000.

4 0

2 years ago

The following are the hypotheses for a test of the claim that college graduation statue and cola preference are independent. H0:

Shkiper50 [21]

Answer:

$\chi^2 = 0.579$

And the critical value for the significance level used is:

$\chi^2_{crit}= 5.991$

Since the calculated value is less than the critical value we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the College graduation status and cola preference are independent

Step-by-step explanation:

For this case we want to test the following hypothesis:

Null hypothesis: College graduation status and cola preference are independent

Alternative hypothesis: College graduation status and cola preference are dependent

For this case we got a calculated statistic of:

$\chi^2 = 0.579$

And the critical value for the significance level used is:

$\chi^2_{crit}= 5.991$

7 0

2 years ago